Chaos Solitons & Fractals最新文献

{"title":"Physical approach to control ion channel in a neuron","authors":"Jun Ma ,&nbsp;Jiarong Zhao ,&nbsp;Binchi Wang ,&nbsp;Chunni Wang","doi":"10.1016/j.chaos.2026.118079","DOIUrl":"10.1016/j.chaos.2026.118079","url":null,"abstract":"<div><div>Blockers and activators can modify the conductance of the ion channels, and the channel currents are changed to regulate the membrane potential of a neuron for presenting different firing patterns. From dynamical aspect, blocking the ion channel and external stimuli are processed by adding equivalent trans-membrane current on the neuron models, however, the physical processing is not clarified. In this article, a control branch shunts channel current from the inductive channel of the FitzHugh-Nagumo (FHN) neural circuit, and external stimuli can be encoded in the ion channel rather than imposing direct forcing currents on the membrane potential. The neural circuit is controlled by shunting current from the inductor of the branch circuit in the FHN neural circuit, a constant voltage connected with a memristor is used to generate forcing current within finite frequency band rather than sole frequency, which is consistent with realistic external stimuli. The control branch circuit composes a capacitor for filtering the external stimulus and the filtered current will interact with the shunted channel current under energy exchange, as a result, changes of the energy ratio between magnetic field and electric field will modify the capacitor voltage, which corresponds to the membrane potential of the neuron model. Energy function is provided to discern the correlation between firing modes and energy level, and then coherence resonance is induced under noisy disturbance. Our results provide new insights into control of ion channels from physical aspect, that is, external energy injection via the control branch circuit (external sub-branch circuit) into the neural circuit tends to build a hybrid ion channel for regulating the energy level of the neurons. As a result, the ion channel becomes controllable following the injection of energy flow and the channel conductance becomes controllable. Therefore, the external energy is encoded in the ion channel for further adjustment in the energy level of the neuron, and then the energy levels control the neural activities.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118079"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evolutionary dynamics of reactive partner strategy in stochastic games","authors":"Jing Zhang ,&nbsp;Yixin Yang ,&nbsp;Zhihai Rong ,&nbsp;Zhi-Xi Wu","doi":"10.1016/j.chaos.2026.118131","DOIUrl":"10.1016/j.chaos.2026.118131","url":null,"abstract":"<div><div>Stochastic games provide an efficient incentive mechanism for the emergence of cooperation by modeling the feedback between environmental states and individual behaviors, where players usually make decisions through memory strategies. In this paper, a mixed memory-one strategy called the reactive partner strategy (<span><math><mrow><mi>R</mi><mi>E</mi><mi>P</mi><mi>A</mi></mrow></math></span>) is introduced into stochastic games, which tends to deterministically cooperate with the cooperative co-player and forgive an opponent’s defection with a probability. By analyzing the payoff relationships between pure memory-one strategies and <span><math><mrow><mi>R</mi><mi>E</mi><mi>P</mi><mi>A</mi></mrow></math></span>, it is shown that <span><math><mrow><mi>R</mi><mi>E</mi><mi>P</mi><mi>A</mi></mrow></math></span> is always a Nash equilibrium strategy that can resist invasion by defective strategies, and the proper forgiving probability of <span><math><mrow><mi>R</mi><mi>E</mi><mi>P</mi><mi>A</mi></mrow></math></span> can promote cooperation under low benefit conditions in stochastic games where the famous pure memory-one strategy of win-stay, lose-shift (<span><math><mrow><mi>W</mi><mi>S</mi><mi>L</mi><mi>S</mi></mrow></math></span>) fails to oppose invasion by defectors. For high benefit values, <span><math><mrow><mi>R</mi><mi>E</mi><mi>P</mi><mi>A</mi></mrow></math></span> can act as an evolutionary bridge that connects always defect (<span><math><mrow><mi>A</mi><mi>l</mi><mi>l</mi><mi>D</mi></mrow></math></span>), <span><math><mrow><mi>G</mi><mi>r</mi><mi>i</mi><mi>m</mi></mrow></math></span> and <span><math><mrow><mi>W</mi><mi>S</mi><mi>L</mi><mi>S</mi></mrow></math></span> strategies, which may offer valuable insights into understanding and promoting both cooperation and strategic evolution in stochastic games.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118131"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147278172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evolution from dissipative soliton resonance to four-wave mixing-assisted supercontinuum in the spatiotemporal mode-locked fiber laser","authors":"Haoxue Qiu,&nbsp;Yong Yao,&nbsp;Linguang Guo,&nbsp;Songting Li,&nbsp;Chengda Ge,&nbsp;Jinwei Zhang,&nbsp;Xiaochuan Xu,&nbsp;Jiajun Tian,&nbsp;Jianan Duan","doi":"10.1016/j.chaos.2026.118088","DOIUrl":"10.1016/j.chaos.2026.118088","url":null,"abstract":"<div><div>To the best of our knowledge, the nonlinear evolution characteristics are first systematically investigated by increasing the pump power without altering the cavity architecture in the isolator-free spatiotemporal mode-locked (STML) Yb-doped fiber laser allowing counter-propagating fields, which reveals the staged activation of multiple nonlinear effects in the experiment. As the pump power increases from 236 mW to 568 mW, self-phase modulation (SPM), stimulated Raman scattering (SRS) and four-wave mixing (FWM) are successively triggered to form the mode-locked properties of dissipative soliton resonance (DSR), SRS-induced dual-wavelength and FWM-assisted supercontinuum. At low pump power of 236 mW, the DSR features triangular spectra, rectangular nanosecond pulses and strong stability under the nonlinear effect of SPM. When the pump power exceeds Raman threshold, a distinct Raman peak emerges near 1070 nm, forming a dual-wavelength STML. The main and Raman pulses exhibit synchronous oscillation and stable STML characteristics, indicating that SRS plays a key role in energy redistribution and mode stabilization. At higher pump power of 568 mW, enhancing nonlinear interactions leads to producing a supercontinuum with a bandwidth exceeding 50 nm, which is attributed to the enhanced FWM effect. Throughout the evolution, the pulse train remains stable with a repetition rate of 4.48 MHz. The results provide a comprehensive understanding of nonlinear evolution in the multimode STML fiber lasers and highlight the significant roles of SPM, SRS, and FWM in the ultrafast multimode fiber laser dynamics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118088"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modification speed and radius of higher-order interactions alter the oscillatory dynamics in an agent-based model","authors":"Thomas Van Giel ,&nbsp;Hanna Jaspaert ,&nbsp;Aisling J. Daly ,&nbsp;Bernard De Baets ,&nbsp;Jan M. Baetens","doi":"10.1016/j.chaos.2026.118017","DOIUrl":"10.1016/j.chaos.2026.118017","url":null,"abstract":"<div><div>Understanding the population dynamics of ecological systems is crucial for predicting shifts in biodiversity and ensuring the protection of these systems. Established models often focus on pairwise species interactions, yet recent studies have highlighted the importance of higher-order interactions (HOIs) in shaping community structure and function. In this study, we investigate the effects of HOIs in an agent-based model with three species engaged in intransitive competition. We introduce an HOI where one species modifies the competition between the other two. We explore the impact of the strength, radius of influence, and speed of this interaction modification on species abundances and oscillations thereof. Our results show that these abundances are not only greatly impacted by the strength, but also by the radius and speed of the interaction modification. A deeper investigation demonstrates that the changes in the oscillations are caused by the interaction modification itself, and not the change in pairwise interaction strength caused by the HOI. These results emphasise the importance of considering the spatio-temporal scales of higher-order interactions when assessing ecosystem stability, highlighting that such interactions can introduce complex dynamical behaviours that go beyond the predictions of traditional pairwise or simpler higher-order models.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118017"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Emergent spatiotemporal dynamics of stochastic FitzHugh–Nagumo neural networks: Random Besicovitch almost periodicity and synchronization","authors":"Tianwei Zhang ,&nbsp;Ting Yuan ,&nbsp;Jianwen Zhou","doi":"10.1016/j.chaos.2026.118042","DOIUrl":"10.1016/j.chaos.2026.118042","url":null,"abstract":"<div><div>The purpose of this study is to investigate the emergent spatiotemporal dynamics of a fully space–time discrete stochastic FitzHugh–Nagumo neural network with time delays under random perturbations and feedback control. To this end, we formulate a discrete stochastic reaction–diffusion network by combining the exponential Euler discretization in time with central finite differences in space, and we introduce a mean-square framework of random Besicovitch almost periodic sequences suitable for stochastic discrete dynamical systems. Based on this framework, a fixed-point approach together with the Boyd–Wong lemma is employed to establish the existence and uniqueness of random Besicovitch almost periodic solutions. Furthermore, sufficient conditions are derived to ensure the local exponential stability of the uncontrolled network, and a state-feedback control scheme is proposed to achieve local exponential synchronization between master–slave networks. Numerical simulations are provided to illustrate the theoretical results and to demonstrate the effects of discretization parameters, stochastic perturbations, and feedback gains on the system dynamics. The novelty of this work lies in introducing random Besicovitch almost periodicity into fully space–time discrete stochastic neural networks with delays, and in unifying stability and synchronization analysis within a single discrete stochastic framework.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118042"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146209827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-image encryption based on an extended chaotic map and a directional shift transformation","authors":"Linian Liu ,&nbsp;Binrong Huang ,&nbsp;Shouliang Lai","doi":"10.1016/j.chaos.2026.118037","DOIUrl":"10.1016/j.chaos.2026.118037","url":null,"abstract":"<div><div>The proposed image encryption method is based on an extended logistic-based chaotic map integrated with a directional shift for enhanced randomness, security, and resistance to cryptographic attacks. Along with the control parameter, the new chaotic sequence, which utilizes two previous values, significantly enhances complexity and unpredictability. This modification, therefore, ensured higher sensitivity to initial conditions and resistance to differential, brute-force, and known plaintext attacks. The encryption scheme incorporated a directional shift transformation to further obscure pixel locations and enhance security. The key matrix decides the number and direction of shifts punctuated on each pixel. The transformation shifted pixels in one of four possible primary directions-lefthand, right-hand, upside-down, or downside. This created a highly unpredictable relocation mechanism, minimizing the correlation between the adjacent pixels in the encrypted images. Due to the implementation of a suitable algorithm for the key extracted from the input image, a slight change in the original image led to huge differences in encryption outputs, assuring statistical and cryptanalytic attacks. Security analyses carried out, including histogram analysis and correlation coefficient computation, have also confirmed the effectiveness of the scheme.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118037"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146209828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correlation-weighted communicability curvature as a structural driver of dengue spread: A Bayesian spatial analysis of Recife (2015–2024)","authors":"Marcílio Ferreira dos Santos ,&nbsp;Cleiton de Lima Ricardo ,&nbsp;Andreza dos Santos Rodrigues de Melo","doi":"10.1016/j.chaos.2026.118089","DOIUrl":"10.1016/j.chaos.2026.118089","url":null,"abstract":"<div><div>We investigate whether functional connectivity in urban road networks explains dengue incidence in Recife, Brazil (2015–2024), beyond traditional adjacency-based spatial dependence. For each neighborhood, we compute the average <em>communicability curvature</em>, a graph-theoretic measure capturing multiscale accessibility through redundant network paths. The curvature metric is incorporated into Negative Binomial models, fixed-effects regressions, SAR/SAC spatial models, and a hierarchical INLA/BYM2 specification. Across all frameworks, curvature emerges as the strongest and most stable predictor of dengue risk. In the BYM2 model, the structured spatial component collapses (<span><math><mrow><mi>ϕ</mi><mo>≈</mo><mn>0</mn></mrow></math></span>), indicating that spatial variation traditionally attributed to CAR adjacency effects is largely absorbed by functional network connectivity. Rather than eliminating spatial dependence, the results suggest a reparametrization of space: dengue diffusion in Recife is structured less by geometric contiguity and more by network-mediated urban connectivity.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118089"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of a density-dependent microorganism flocculation model with diffusion","authors":"Zhihong Zhao ,&nbsp;Lingling Xu ,&nbsp;Ke Guo","doi":"10.1016/j.chaos.2026.118101","DOIUrl":"10.1016/j.chaos.2026.118101","url":null,"abstract":"<div><div>This study comprehensively investigates a microorganism flocculation model that incorporates diffusion processes and density-dependent growth. We analyze the boundary equilibrium, positive equilibria and Turing instability to model the removal, continuous collection and distribution of microorganisms. For the ordinary differential equation (ODE) version, we analytically establish that the equilibrium undergoes forward and backward bifurcations. Meanwhile, we delve into the local and global stability of the microorganism-free state (boundary equilibrium) and coexistence state (positive equilibria), as well as examine the existence of Hopf bifurcations at the positive equilibrium, which indicate periodic oscillatory behaviors. Moreover, for the partial differential equation (PDE) system extended with spatial diffusion, we derive the conditions for Turing instability and establish the conditions leading to Turing–Hopf bifurcations. Finally, we provide numerical studies to illustrate and support our theoretical findings.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118101"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146778803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Event-triggered cooperative control of connected vehicle platoons with distributed unbounded communication delays and unknown external disturbances","authors":"Ya Deng ,&nbsp;Wei Zhu ,&nbsp;Qianghui Zhou ,&nbsp;Chenlu Wang","doi":"10.1016/j.chaos.2026.118049","DOIUrl":"10.1016/j.chaos.2026.118049","url":null,"abstract":"<div><div>This paper addresses the cooperative control of a platoon of leader-following connected vehicles under an observer-based event-triggered control strategy, incorporating distributed unbounded communication delays and unknown external disturbances. Given the unavailability or limitations of direct access to the internal states and external disturbances, an extended state observer is designed to reconstruct the system states. This observer employs the relative outputs of neighboring vehicles to estimate the states of the follower vehicles and the external disturbances simultaneously. Based on these estimations, an event-triggered platoon control scheme in the presence of distributed unbounded communication delays is introduced, which can prevent continuous updates of controller. This scheme ensures the achievement of the platoon control objective while excluding Zeno-behavior in the event-triggering sequence. Finally, theoretical analysis is effectively supported via a simulation example.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118049"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reconstructing multiplex networks with higher-order interactions from dynamics","authors":"Weifang Huang,&nbsp;Ying Xie,&nbsp;Zhiqiu Ye,&nbsp;Xuening Li,&nbsp;Ya Jia,&nbsp;Xuan Zhan","doi":"10.1016/j.chaos.2026.118120","DOIUrl":"10.1016/j.chaos.2026.118120","url":null,"abstract":"<div><div>Multiplex networks provide an important framework for characterizing multilevel interactions in complex systems, yet reconstructing their structures from dynamical data remains a challenging task. In this work, we propose a unified regression-based framework for multiplex network reconstruction grounded in nodal dynamics and coupling functions. By extending the node-wise regression reconstruction of Malizia et al. (2024) from single-layer systems to multiplex settings, the framework can simultaneously reconstruct intra-layer pairwise interactions, higher-order interaction structures, and one-to-one inter-layer couplings from observed time-series data. Numerical experiments based on the Hindmarsh–Rose neuronal model demonstrate that the proposed method achieves reliable reconstruction performance for directed weighted, undirected unweighted, and higher-order multiplex networks. Furthermore, applications to the Padgett–Florentine families multiplex social network confirm the robustness and generalization capability of the framework under real-world network topologies. Overall, this study provides a general and robust approach for systematically reconstructing multiplex networks and their higher-order interaction structures from time-series data.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118120"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}